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In a book Conceptual Wavelets in Digital Signal Processing by Lee Fugal 2009 on page 246 the author talks about aliasing present in DWT subbands due to downsampling by 2 and states:

Recall from DSP that for a signal at 0.3 Nyquist aliasing from downsampling will "reflect" the signal across Nyquist. Thus we see the aliasing components at Nyquist minus 0.3 Nyquist or 0.7 Nyquist.

I thought it was safe to downsample a signal below 0.5 Nyquist by 2, isn't that correct ? Also on the image below the signal at 0.3 Nyquist and the alias at 0.7 Nyquist have different amplitudes.

enter image description here

I would think the aliasing in approximations can only occur because of imperfect filtering i.e. because some of the high frequencies above 0.5 Nyquist were also captured before downsampling by 2. But the author also shows using UDWT ( undecimated DWT ) with the same filters that without downsampling approximations after filtering have only frequencies around 0.3 Nyquist:

enter image description here

So where does aliasing come from in DWT in this example?

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  • $\begingroup$ image below? please edit your question to add the image you refer to. $\endgroup$ – user28715 May 22 '19 at 13:46
  • $\begingroup$ @StanleyPawlukiewicz sorry, added $\endgroup$ – Anton B May 22 '19 at 14:16
  • $\begingroup$ Your misunderstanding stems from the term Nyquist... $\endgroup$ – Fat32 May 22 '19 at 22:24
  • $\begingroup$ @Fat32 I thought the term Nyquist here had meaning of half of the sampling frequency and so equals to 1 pi rad/sample. Thus the signal bandwidth is limited to 0.5 pi rad/sample or pi / 2 rad/sample and so downsampling by 2 is safe. $\endgroup$ – Anton B May 23 '19 at 10:41
  • $\begingroup$ Oh I'm quite sorry that's OK! So you are right in your confusion... Because it's really a confusing statement... Imho the best to do is to formulate all possible meanings from that compact frame and see which one is consistent with the rest of the text... $\endgroup$ – Fat32 May 23 '19 at 18:47

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